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Each Insufficient in Its Own Way: Calibrating Language Models Across Varying Evidence States

Jiayi Li, Dennis L. Shung, Bradly C. Stadie

arXiv:2610.33237v1cs.CL

TL;DR

Language models need to judge whether their current evidence is enough to answer, but most calibration work holds the evidence fixed. SuffiCE trains pre-answer confidence across evidence states, and improves calibration across clinical diagnosis and multi-hop question answering. The authors conclude that confidence can respond to which evidence is present, not just its amount.

  • Problem

    Most calibration work treats each question’s evidence as fixed, leaving untested whether confidence changes appropriately as evidence changes.

    Source: §1 · p. 1

  • Method

    SuffiCE trains a model’s pre-answer next-token probability against its empirical success rate across granular evidence states.

    Source: §1 · p. 2

  • Results

    SuffiCE reduces the Brier score of the base logit by up to 60% and increases AUROC by up to 0.16.

    Source: §1 · p. 2

  • Takeaways & Limitations

    SuffiCE’s confidence rises with decisive evidence rather than every added piece, supporting the conclusion that models can judge whether current evidence is enough to answer.

    Source: §6 · p. 8

    SuffiCE has not been tested in real clinical scenarios, and its confidence should not replace clinical judgment.

    Source: Limitations · p. 9

Abstract

from arXiv · show

How can a language model know whether it has enough evidence to answer? Language models tend to answer even when the evidence they have is insufficient. Deciding whether to answer or gather more evidence requires a calibrated estimate of how likely an answer is to be correct with the available evidence. However, most calibration work treats the input as fixed, without asking how this estimate should change with the evidence. We introduce \emph{evidence-state calibration}, which requires a model's confidence before answering to match its probability of answering correctly and to change accordingly whenever the evidence changes this probability. We propose \ours{} (\textbf{Suffi}ciency \textbf{C}onfidence \textbf{E}stimation), which fine-tunes the confidence already present in a model's next-token distribution to match how often the model answers correctly from each evidence state. Across clinical diagnosis and multi-hop question answering with four models from two families, \ours{} reduces the Brier score by up to 60\% and increases AUROC by up to 0.16. Its confidence matches the empirical success rate and responds not only to the amount of evidence but also to which evidence is present, showing that models can learn to judge whether their current evidence is enough to answer.

1 Introduction

A model deciding whether to answer or gather more evidence needs confidence that reflects the available evidence, but most calibration work holds evidence fixed. This section defines evidence-state calibration and introduces SuffiCE, which trains pre-answer confidence against success across varied evidence states.

1 Introduction

  • Before answering, a model must judge whether its information is enough; in high-stakes diagnosis, testing may reveal a different cause than an initial impression suggests.The paper illustrates this with fatigue that may appear consistent with iron deficiency but could be associated with celiac disease.Source: §1 · p. 1
  • Most calibration work holds evidence fixed, so it cannot test whether confidence changes appropriately as available information evolves.In interactive settings, models must decide at each turn whether to answer or gather more evidence.Source: §1 · p. 1
  • Evidence-state calibration requires pre-answer confidence to match the probability of answering correctly and change by the same amount when evidence changes that probability.Figure 1 illustrates calibrated confidence matching correctness across two evidence sets, unlike confidence that mismatches the change.Source: Figure 1 · p. 1, §1 · p. 2
  • The paper constructs granular evidence states for each problem, varying both evidence amount and combinations, and measures sufficiency by the model’s success rate in each state.This captures that some incomplete states remain answerable while others omit a decisive piece of evidence.Source: §1 · p. 2
  • SuffiCE trains confidence already present in the model’s next-token distribution against success rates across evidence states, without an added classifier or generated confidence number.Its confidence is the model’s probability of choosing to answer rather than request more information.Source: §1 · p. 2
  • SuffiCE reduces the Brier score of the base logit by up to 60% and increases AUROC by up to 0.16 across clinical diagnosis and multi-hop question answering.It improves calibration for every evaluated model and dataset; answering only when SuffiCE is confident gives fewer wrong answers than any baseline.Source: §1 · p. 2

2 Related Work

Related work addresses evidence acquisition, input sufficiency, and confidence calibration, but does not jointly train confidence to track success across changing evidence states. This paper positions its approach as measuring model-specific success across controlled states that vary in evidence amount and type.

2 Related Work

  • The paper connects interactive information seeking, input sufficiency, and confidence calibration as related lines of work addressing whether current evidence supports an answer.Each line addresses a different part of the answer-or-gather decision.Source: §2 · p. 2

Interactive information seeking

  • Interactive information-seeking methods use confidence or uncertainty to decide whether to gather more information, while this approach estimates success before generating an answer across controlled states.LA-CDM instead uses verbalized confidence about a hypothesis already generated.Source: §2 · p. 2

Information sufficiency and unanswerability

  • Prior sufficiency and unanswerability work often assigns binary sufficiency labels to inputs, whereas this paper defines sufficiency by how often the answering model succeeds from each state.This accounts for models answering correctly from some inputs labeled insufficient.Source: §2 · p. 3

Confidence calibration

  • Existing calibration methods do not explicitly train confidence to track success across changing evidence states; this work varies both evidence amount and type in controlled states.Zhang et al. (2026) evaluate confidence as hints accumulate in a fixed sequence but do not train on changing states.Source: §2 · p. 3

3 Method

SuffiCE trains confidence from evidence states, each pairing a question with the evidence currently available, to reflect both answer success and how success changes across states. It estimates success from repeated answers by a fixed policy, then trains the model’s own answer-versus-seek probability to predict that rate before answering.

3.1 Problem Formulation

  • A state pairs a question with available evidence, and its sufficiency depends on whether the model can answer correctly—not on whether the evidence is complete.The same state may be sufficient for one model and insufficient for another.Source: §3.1 · p. 3

3.2 Evidence States

  • Evidence states for each problem share its question and gold answer but vary in evidence, letting the model learn which evidence makes a correct answer reachable.States vary in both evidence amount and composition, including combinations that hold amount fixed while changing which evidence is present.Source: §3.2 · p. 3
  • Evidence-state calibration requires confidence to match average success at a given confidence and to change by as much as success changes between states of the same problem.The two criteria distinguish pooled calibration from sensitivity to evidence changes within a problem.Source: §3.2 · pp. 3–4

3.3 Monte Carlo Estimation of Success Probability

  • The target for each state is the mean correctness of K independently sampled answers from the fixed answering policy, an unbiased estimate of its success probability.The estimate is specific to that policy and uses the gold answer only during training.Source: §3.3 · p. 4

3.4 Sufficiency Confidence Estimator

  • SuffiCE reads confidence from the model’s next-token probabilities for answering versus seeking more information, then trains that confidence to match the empirical success rate with soft-label binary cross-entropy.It uses no separate classifier head or generated confidence number.Source: §3.4 · pp. 4–5
  • Because binary cross-entropy is strictly proper and the success-rate labels are unbiased, expected loss is minimized when confidence equals the policy’s true success probability.Lower training loss also bounds errors in average success and in how confidence changes across states.Source: §3.4 · p. 5

4 Experimental Setup

The experiments cover two clinical diagnosis datasets and one multi-hop question-answering dataset, with evidence states tailored to each task. Four models are evaluated against confidence baselines using calibration, ranking, and evidence-change metrics.

Datasets

  • Evaluation spans MIMIC and MedQA clinical diagnosis tasks and MuSiQue multi-hop question answering, with all states of a problem kept in one split to prevent leakage.MIMIC uses four abdominal-disease options; MedQA uses USMLE questions, and MuSiQue composes multi-hop questions over Wikipedia.Source: §4 · p. 5

Evidence states

  • Clinical evidence states add different subsets of case sections to the history, while MuSiQue states vary which of three supporting paragraphs are present.MuSiQue includes chain and branching questions, and distractors pad states to three paragraphs so paragraph count and position do not reveal the state.Source: §4 · p. 5, Figure 3 · p. 5

Models and baselines

  • Four answering models are tested: three Qwen models of increasing size and Kimi K2.6; each model also serves as its own estimator, with success rates estimated from 10 sampled answers per state.Baselines are the untrained answer-versus-seek probability, verbalized confidence, and Platt scaling of the base logit.Source: §4 · pp. 5–6

Metrics

  • Brier score measures confidence error, AUROC measures ranking of correct above incorrect answers, and change correlation tests whether confidence follows success across states of the same problem.Table 1 reports results for the four models across three datasets as mean ± SD over three seeds.Source: §4 · p. 6, Table 1 · p. 6

5 Results

SuffiCE improves calibration and evidence sensitivity across the reported settings, while evidence-state training helps it distinguish decisive information from merely additional information.

5.1 Overall Performance

  • 20–60% lower Brier score than the base logit and 5–28% lower than Platt scaling; AUROC rises by up to 0.16, and change correlation exceeds every baseline.SuffiCE achieves the best result on every metric in every setting; Figure 4 shows calibration moving toward the ideal diagonal across datasets.Source: §5.1 · pp. 6–7, Figure 4 · p. 6
  • SuffiCE is most accurate at nearly every percentage of questions answered, and its highest-confidence MIMIC answers are almost always correct.Table 2 reports accuracy when answering the specified percentage of the most confident questions.Source: §5.1 · p. 7, Table 2 · p. 7

5.2 Ablation

  • The full-state-only estimator is outperformed by SuffiCE on every metric and dataset, with training epochs matched and also with training steps matched.The ablation estimator learns which problems are hard but never sees missing evidence.Source: §5.2 · p. 7, Figure 5 · p. 7

5.3 Evidence-State Analysis

  • On chain questions, SuffiCE stays low until final hop e3 arrives, while the base logit reaches 0.71 on {e1, e2} despite only 0.06 success.On branching questions, it stays low for either branch alone and for both without e3; it is not given question type or hop assignments.Source: §5.3 · p. 7, Figure 6 · p. 7
  • With two paragraphs in every state, SuffiCE stays low for {e1, e2} and rises when e3 is present, unlike the similarly confident base logit.Success is high only when the final hop e3 is among the two supporting paragraphs.Source: §5.3 · p. 7, Figure 7 · p. 8
  • In the MedQA case, SuffiCE stays uncertain with the X-ray and becomes confident only after biopsy confirms Hirschsprung disease.The X-ray suggests obstruction but cannot distinguish Hirschsprung disease from other causes; the biopsy finds no ganglion cells.Source: §5.3 · p. 8, Table 3 · p. 8

5.4 Cross-Policy Confidence Estimation

  • A Qwen 27B estimator matches or exceeds Kimi K2.6’s own estimate in Brier score on every dataset, and in ρ∆ on MedQA and MuSiQue.It was trained on Kimi K2.6’s success rates without seeing its answers; smaller estimators were less accurate.Source: §5.4 · p. 8, Figure 8 · p. 8

6 Conclusion

SuffiCE trains pre-answer confidence to be calibrated across changing evidence states. Its confidence rises with decisive evidence rather than every added piece, a step toward judging when evidence is enough in high-stakes settings.

6 Conclusion

  • SuffiCE trains a model’s pre-answer confidence to be calibrated across varying evidence states, where confidence must track the probability of answering correctly as evidence changes.The paper presents this as the first work of its kind, to the authors’ knowledge.Source: §6 · p. 8

Limitations

The evaluation uses preconstructed evidence states rather than live multi-turn evidence gathering, and SuffiCE has not been tested in real clinical scenarios.

Limitations

  • Evidence states are preconstructed rather than gathered in live multi-turn interactions; this controlled setting attributes success and confidence differences to the evidence itself.The authors also estimate each target from ten sampled answers per state, and more samples would give more precise targets.Source: Limitations · p. 9
  • SuffiCE has not been tested in real clinical scenarios, and its confidence should not replace clinical judgment.Source: Limitations · p. 9

A.1 Datasets

The evaluation spans clinical diagnosis and multi-hop question answering, with evidence states designed to vary in amount and composition. Success rates differ by dataset and answering policy, and estimates from ten answers per state are sufficiently precise for comparing estimators.

A.1 Datasets

  • Across datasets, Qwen3.5-9B’s mean test success rate ranges from 0.81 on MIMIC to 0.25 on MuSiQue, spanning settings where most states succeed and where most do not.MedQA’s mean is 0.50.Source: §A.1 · p. 13
  • The evaluation uses two clinical diagnosis datasets, MIMIC and MedQA, and the three-hop MuSiQue question-answering dataset.MIMIC uses emergency admissions for four abdominal diseases; MedQA uses OSCE-style diagnosis cases; MuSiQue uses three-hop questions with sampled distractors.Source: §A.1 · p. 13
  • MuSiQue’s branching questions allow evidence e2 alone to be useful, unlike chain questions where e2 is useful only after e1.This gives the evidence-state design distinct combinations of information, not just successive accumulation.Source: §A.1 · p. 13, Table 5 · p. 13

A.2 Answering Policies

  • The main experiments use each model as both answerer and estimator, evaluating every method against that same model’s success-rate targets.Targets are fractions correct across 10 sampled answers per evidence state; cross-policy evaluation is the stated exception.Source: §A.2 · p. 14
  • The same evidence state can have different target success rates across answering models, with differences small on MIMIC but wide on MedQA and MuSiQue.Methods are therefore compared within each model against its own targets.Source: §A.2 · p. 14
  • SuffiCE’s Brier score is over 13 times the estimated sampling-noise floor on every dataset, so sampling noise accounts for only a small part of estimator error.The floor estimates the expected Brier score of a perfect estimator evaluated against success rates from ten answers.Source: §A.2 · p. 14, Table 6 · p. 14

A.3 Training Details

SuffiCE is trained and evaluated using shared prompting and grading procedures, while calibration curves and selective answering assess its behavior across models. Across these analyses, it improves calibration, performs well when answering selectively, and outperforms a step-matched full-evidence-only estimator.

A.3 Training Details

  • All models run with thinking disabled, sample answers at temperature 1.0 without top-p or top-k truncation, and use a rank-32 LoRA estimator initialized to leave the base logit unchanged.The shared settings apply across models and datasets; the answering model itself is the estimator base except in the cross-policy experiment.Source: §A.3 · p. 14, Table 7 · p. 14

B.1 Sufficiency Confidence

  • The sufficiency prompt asks whether current information is enough to answer correctly, using A for sufficient and S for insufficient.The estimator and base logit read the probability of A as the first reply token.Source: §B.1 · p. 15

B.2 Answering / B.3 Verbalized Baseline

  • The answering prompts elicit a diagnosis for clinical cases or a short answer for MuSiQue, while verbalized confidence separately requests a probability of answering correctly without more information.The verbalized baseline reads the first number in the reply as confidence.Source: §B.2 · p. 15, §B.3 · p. 15

B.4 LLM Judges

  • MedQA answers and non-exact-match MuSiQue answers are judged by an LLM, while MIMIC answers use exact matching; all methods for a model share the same grades.The physician judge accepts equivalent diagnoses, but rejects broader categories that do not identify the required diagnosis.Source: §A.3 · p. 14, §B.4 · p. 15

C.1 Calibration Curves for All Models

  • SuffiCE moves every calibration curve toward the diagonal, including curves for Qwen models and Kimi K2.6.Its confidence spans low values on MuSiQue and concentrates near the top on MIMIC, matching the datasets’ success-rate ranges.Source: §C.1 · p. 17, Figure 9 · p. 17

C.2 Selective Answering for All Models

  • Across all four answering models and three datasets, SuffiCE has the highest accuracy at most percentages of questions answered.The smallest margin is for Qwen3.5-4B on the clinical datasets.Source: §C.2 · p. 17, Figure 9 · p. 17

C.3 Step-Matched Ablation

  • SuffiCE remains better on every metric and dataset than a full-only estimator trained for the same number of steps.This step-matched ablation attributes the gap to training across evidence states rather than the number of updates.Source: §C.3 · p. 17, Table 9 · p. 17

C.4 Additional Evidence-State Analysis

SuffiCE’s confidence tracks both the size and direction of evidence-related changes in answerability, and evidence-specific rankings transfer across the two clinical datasets. The proof material explains why calibration alone can miss within-problem changes and why the training loss controls both components of error.

C.4 Additional Evidence-State Analysis

  • SuffiCE has the lowest ∆MAE in 11 of 12 model-dataset combinations and the highest ρwithin for every combination.The Kimi K2.6-on-MIMIC exception for ∆MAE reflects small success changes across many state pairs; ρ∆ still favors SuffiCE there.Source: §C.4 · p. 18

C.5 Cross-Domain Transfer

  • In both clinical transfer directions, the transferred estimator ranks states better than the base logit in AUROC and ρ∆ and recovers about half of the in-domain ρwithin gain.This indicates that what SuffiCE learns about which evidence settles a case carries across datasets.Source: §C.5 · pp. 18–19
  • Overall success level does not transfer: confidence stays near the training dataset’s success rate, so ranking transfers while calibration does not.MIMIC-trained confidence is too high on MedQA; MedQA-trained confidence is too cautious on MIMIC and calibrates worse than the base logit.Source: §C.5 · p. 19

D Proofs / The left side is the mean squared error over all

  • The proof decomposes confidence error into error in each problem’s average success and error in how confidence changes between states of that problem.The second component is half the average squared change gap across ordered state pairs; calibration alone does not remove it.Source: D Proofs · p. 20, The left side is the mean squared… · pp. 20–21

The left side is the mean squared error over all

  • The state-average identity weights each problem by its share of all states, rather than averaging problems equally when their numbers of states differ.Averaging within each problem and then applying the mi/N weights recovers the average over all states.Source: D Proofs · p. 20

D.2 Proof of Corollary 1

The corollary relates excess expected training loss to confidence error across evidence states. Its bound applies over the states included in the loss, motivating training on many evidence states rather than full states alone.

D.2 Proof of Corollary 1

  • The minimum expected loss is reached exactly when confidence equals the answering policy’s success probability at every evidence state.The policy-dependent entropy term is fixed, while the divergence term vanishes only at that equality.Source: §D.2 · pp. 21–22
  • Reducing training loss lowers an upper bound on both average-success error and error in confidence changes between states of the same problem.The bound holds only over states averaged in the loss, which is why SuffiCE trains across many evidence states rather than full states alone.Source: §D.2 · p. 22, Table 12 · p. 23

E Comparison with Related Work

SuffiCE combines pre-answer confidence from the model’s own next-token probability with training and evaluation across controlled evidence states. Prior methods lack one or more of these properties, and the paper argues that training across states matters for learning which evidence determines success.

E Comparison with Related Work

  • SuffiCE calibrates the model’s own pre-answer probability of answering, using controlled evidence subsets and within-problem evaluation.The comparison identifies five properties and says no prior method has all five.Source: E Comparison with Related Work · p. 23
  • P(IK) and pre-generation probes estimate success before answering but use an added head or probe; calibration tuning and P(Sufficient) score after an answer exists.P(IK) (Kadavath et al., 2022), pre-generation probes (Lugoloobi et al., 2026), calibration tuning (Kapoor et al., 2024), and P(Sufficient) (Zhang et al., 2026) each lack at least one of SuffiCE’s properties.Source: E Comparison with Related Work · p. 23
  • Training on controlled evidence subsets lets SuffiCE learn which evidence decides success, while within-problem evaluation tests whether confidence follows success across states.The paper reports that a full-only estimator with the same formulation falls short of SuffiCE.Source: E Comparison with Related Work · p. 23

F.1 MuSiQue Case Studies

In two MuSiQue case studies, SuffiCE’s confidence tracks sampled answer success across incomplete and complete evidence states, unlike base logits that can rise despite no sampled correct answers. The appendix provides full case inputs and evidence-state layouts; the clinical experiments use restricted MIMIC-IV-Ext data, and SuffiCE is not intended for clinical use.

F.1 MuSiQue Case Studies

  • With both branches but not the final hop, neither case has a sampled correct answer; base logits rise to 0.50 and 0.98, while SuffiCE stays at or below 0.02 and reaches only 0.16.Once the final hop is shown, the first case’s base logit falls to 0.11 despite 20% sampled success, and the second remains at 0.96 despite 30% success.Source: §F.1 · p. 24
  • 0.04: SuffiCE’s confidence on the two full-evidence questions matches their different success rates within this margin, while base logits miss in opposite directions.For the Senate question, 20% of sampled answers are correct and SuffiCE gives 0.19; for the Dutch arrival question, the rate is 30% and SuffiCE gives 0.34.Source: §F.1 · p. 24

F.2 Full Evidence States of the Case Studies

  • The full-input appendix shows evidence states by supporting facts, with the second case highlighting the state containing both branches but not the final hop.The model sees the question and evidence in input order, not the analysis-only state labels; the MuSiQue paragraphs are shuffled into a fixed order.Source: Table 13 · p. 24, Table 14 · p. 24, §F.2 · p. 24

G Ethical Considerations

  • The clinical experiments use deidentified MIMIC-IV-Ext data under a PhysioNet data-use agreement, do not release the data, and are not intended for clinical use.Source: G Ethical Considerations · p. 27

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